An example of this process can be found at Key Length which uses multiple reports to suggest that a symmetric cipher with 128 bits, an asymmetric cipher with 3072 bit keys, and an elliptic curve cipher with 512 bits, all have similar difficulty at present.

Common families include symmetric systems ( e. g. AES ) and asymmetric systems ( e. g. RSA ); they may alternatively be grouped according to the central algorithm used ( e. g. elliptic curve cryptography ).

An ellipse is a smooth closed curve which is symmetric about its horizontal and vertical axes.

" Universal Resonance Curve ", a symmetric approximation to the normalized response of a resonant circuit ; abscissa values are deviation from center frequency, in units of center frequency divided by 2Q ; ordinate is relative amplitude, and phase in cycles ; dashed curves compare the range of responses of real two-pole circuits for a Q value of 5 ; for higher Q values, there is less deviation from the universal curve.

In electrical engineering, this approximate symmetric response is known as the universal resonance curve, a concept introduced by Frederick E. Terman in 1932 to simplify the approximate analysis of radio circuits with a range of center frequencies and Q values.

It is a symmetric logistic distribution curve, often confused with the " normal " gaussian function.

It first appeared in " Nuclear Energy and the Fossil Fuels ," geologist M. King Hubbert's 1956 presentation to the American Petroleum Institute, as an idealized symmetric curve, during his tenure at the Shell Oil Company.

The graph of a Gaussian is a characteristic symmetric " bell curve " shape that quickly falls off towards plus / minus infinity.

If the sum of the degrees of x and y in each term is always even or always odd, then the curve is symmetric about the origin and the origin is called a center of the curve.

There are, in fact, two ways to measure the spherical area enclosed by a simple closed curve, but the inequality is symmetric with the respect to taking the complement.

We now observe two facts: Since is a hyperelliptic curve the map from the symmetric product

Gram was the first mathematician to provide a systematic theory of the development of skew frequency curves, showing that the normal symmetric Gaussian error curve was but one special case of a more general class of frequency curves.

This formula, a symmetric weighted sum credited to Glenn Davis, is based on the fact that any point on the curve must be a linear combination of the ends.

In symmetric unimodal distributions, such as the normal ( or Gaussian ) distribution ( the distribution whose density function, when graphed, gives the famous " bell curve "), the mean ( if defined ), median and mode all coincide.

; Cryptography: Commonly used symmetric key algorithms like DES, Triple DES, AES, and asymmetric key algorithms such as RSA, elliptic curve cryptography are supported as well as other cryptographic services like signing, key generation and key exchange.

A leased line is a service contract between a provider and a customer, whereby the provider agrees to deliver a symmetric telecommunications line connecting two or more locations in exchange for a monthly rent ( hence the term lease ).

An arc connecting node A to B implies not only that " A is relevant to B ", but also that " B is relevant to A " ( i. e., relevance is a symmetric relationship ).

In geometry an Archimedean solid is a highly symmetric, semi-regular convex polyhedron composed of two or more types of regular polygons meeting in identical vertices.

There are four cases which need to be considered, of which two are symmetric to the other two.

But they have three panes including a command line pane below ( or hidden behind ) two symmetric panes.

* If f is an irreducible polynomial of prime degree p with rational coefficients and exactly two non-real roots, then the Galois group of f is the full symmetric group S < sub > p </ sub >.

If the particles are bosons, they occupy a totally symmetric state, which is symmetric under the exchange of any two particle labels:

In contrast, the Coulomb repulsion of the electrons, i. e. the tendency that they try to avoid each other by this repulsion, would lead to an antisymmetric orbital function ( i. e. with the-sign ) of these two particles, and complementary to a symmetric spin function ( i. e. with the + sign, one of the so-called " triplet functions ").

Multihulls include: Proas, which have two differently shaped or sized hulls with lateral symmetry ; catamarans, which have two hulls with longitudinal symmetry ; and trimarans, which have a main hull in the center and symmetric stabilizing hulls on either side.

A more symmetric way to describe the situation is the following: Alice has one particle, Bob two, and Carol one.

With this distance, the set of n-node binary trees becomes a metric space: the distance is symmetric, positive when given two different trees, and satisfies the triangle inequality.

In the symmetric TSP, the distance between two cities is the same in each opposite direction, forming an undirected graph.

Notationally, this is written as T < sup > 2 </ sup >/ S < sub > 2 </ sub > – the 2-torus quotiented by the group action of the symmetric group on two letters ( switching coordinates ), and it can be thought of as the configuration space of two unordered points on the circle, possibly the same ( the edge corresponds to the points being the same ), with the torus corresponding to two ordered points on the circle.

Disulfides where the two R groups are the same are called symmetric, examples being diphenyl disulfide and dimethyl disulfide.

There are two types: asymmetric wave ripples and symmetric current ripples.

This is in contrast to symmetric warfare, where two powers have similar military power and resources and rely on tactics that are similar overall, differing only in details and execution.

No two gamma-ray burst light curves are identical, with large variation observed in almost every property: the duration of observable emission can vary from milliseconds to tens of minutes, there can be a single peak or several individual subpulses, and individual peaks can be symmetric or with fast brightening and very slow fading.

In computing, symmetric multiprocessing ( SMP ) involves a multiprocessor computer hardware architecture where two or more identical processors are connected to a single shared main memory and are controlled by a single OS instance.

Tracks primarily consist of two straights and four left-turn corners, few tracks are symmetric and often the shape parallels that of an egg or a tri-oval.

This can be seen in the more Roman-influenced Federal structure's ornate, colossal Corinthian columns of its façade, which is also embellished by Corinthian pilasters and a symmetric arrangement of sash windows piercing the two stories of the façade.

However, every identity matrix with at least two rows and columns has an infinitude of symmetric square roots .< ref > Mitchell, Douglas W. " Using Pythagorean triples to generate square roots of I < sub > 2 </ sub >".

However, the irreducible representations of the symmetric group are not known in arbitrary characteristic.

The determination of the irreducible modules for the symmetric group over an arbitrary field is widely regarded as one of the most important open problems in representation theory.

More generally the Cartan-Helgason theorem gives the decomposition when G / H is a compact symmetric space, in which case all multiplicities are one ; a generalization to arbitrary σ has since been obtained by.

The conjugate gradient method can be applied to an arbitrary n-by-m matrix by applying it to normal equations A < sup > T </ sup > A and right-hand side vector A < sup > T </ sup > b, since A < sup > T </ sup > A is a symmetric positive-semidefinite matrix for any A.

Thus s < sub > p </ sub > is a geodesic symmetry and, since p was arbitrary, M is a Riemannian symmetric space.

While the quaternionic projective plane with its symmetric metric has a middle-dimensional stable systolic ratio of 10 / 3, the analogous ratio for the symmetric metric of the complex projective 4-space gives the value 6, while the best available upper bound for such a ratio of an arbitrary metric on both of these spaces is 14.